Altitudes of a Tetrahedron and Traceless Quadratic Forms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2013
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| _version_ | 1866916119641587712 |
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| author | Havlicek, Hans Weiß, Gunter |
| author_facet | Havlicek, Hans Weiß, Gunter |
| contents | It is well known that the three altitudes of a triangle are concurrent at the so-called orthocenter of the triangle. So one might expect that the altitudes of a tetrahedron also meet at a point. However, it was already pointed out in 1827 by the Swiss geometer Jakob Steiner (1796--1863) that the altitudes of a general tetrahedron are mutually skew, for they are generators of an equilateral hyperboloid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_0179 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Altitudes of a Tetrahedron and Traceless Quadratic Forms Havlicek, Hans Weiß, Gunter Metric Geometry 51N20 It is well known that the three altitudes of a triangle are concurrent at the so-called orthocenter of the triangle. So one might expect that the altitudes of a tetrahedron also meet at a point. However, it was already pointed out in 1827 by the Swiss geometer Jakob Steiner (1796--1863) that the altitudes of a general tetrahedron are mutually skew, for they are generators of an equilateral hyperboloid. |
| title | Altitudes of a Tetrahedron and Traceless Quadratic Forms |
| topic | Metric Geometry 51N20 |
| url | https://arxiv.org/abs/1304.0179 |